A commentary ``On the periodic solutions of a forced second-order equation'' by S. P. Hastings and J. B. McLeod (Q1322679)

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scientific article; zbMATH DE number 563419
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A commentary ``On the periodic solutions of a forced second-order equation'' by S. P. Hastings and J. B. McLeod
scientific article; zbMATH DE number 563419

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    A commentary ``On the periodic solutions of a forced second-order equation'' by S. P. Hastings and J. B. McLeod (English)
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    28 May 1995
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    In this short note, the authors comment on the relationship of the analytical methods (shooting and perturbation) used by Hastings and McLeod in the paper ``On the periodic solutions of a forced second-order equation'' [ibid. 225-245 (1991; Zbl 0801.34040)] to the geometrical approach of nonlinear dynamical systems theory. Their bridge between analysis and geometry is a global perturbation method known as Melnikov's method. Some questions arising from the methods of Hastings and McLeod and their relationship to the more geometrical methods of dynamical systems theory are given by the authors.
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    adiabatic dynamical system
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    smale horseshoe
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    homoclinic tangle
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    geometrical approach
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    nonlinear dynamical systems theory
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    global perturbation method
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    Melnikov's method
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